A method for selection and use of numerical integration points for molecules with cylindrical symmetry

Boys and Handy [1] have discussed the solution of the bivariational equations with restricted numerical integration. One of the weaknesses of the method was that in the numerical summations over points, some points arose with r _ij= 0 and non-zero weights. This makes the method quite impractical for the Schrodinger Hamiltonian (because of the singularity at r _ij= 0), and it cannot be advantageous for the transcorrelated Hamiltonian C^–1HC because there will be some discontinuous higher derivatives at r _ij=0. Here it is shown how the symmetry of cylindrically symmetric molecules can be used to eliminate such points, without losing any of the advantages of the overall method, such as the convergence of the eigensolutions. It is also shown how the primary numerical integration points (z _i, r_i) may be chosen in any calculation such that each is associated with an equal amount of one-electron density. The choice of the angular coordinates are governed by the removal of the r _ij=0 points and maintaining the natural orthogonality between orbitals of different symmetry types. The method has been programmed and found to be practical, although no new molecular calculations have yet been performed. It is to be hoped that these points will give a basis for new transcorrelated calculations on diatomic molecules.This paper was presented during the session on numerical integration methods for molecules of the 1970 Quantum Theory Conference in Nottingham. It has been revised in the light of the interesting discussion which followed.     

Reduction of ketones with secondary alcohols,catalyzed by triphenylphosphine complexes of ruthenium and rhodium

Russian Chemical Bulletin -     

Skeletal ruthenium catalyst in asymmetric hydrogenation

Conclusions Skeletal ruthenium catalyst, modified with D-(+)-tartaric acid, leads to the asymmetric hydrogenation of the carbonyl group in acetoacetic ester.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, p. 2361, October, 1972.     

Reaction of onium salts with nucleophilic reagents

Russian Chemical Bulletin -     

The ultraviolet spectra of silocyclobutanes

The UV spectra of Si-substituted silocyclobutanes in vacuum were studied. The bathochromic shift of the absorption band, disclosed by comparison with bands of the corresponding acyclic compounds, can be explained by the highly strained state of the four-membered ring. This same principle in disilocyclobutanes leads to the reduction of the barrier effect of the methylene group, disrupting the interaction of the silicon atoms in the unstrained molecule.     

Derivatives of metal carbonyls containing a metal-o-carborane σ-bond

Russian Chemical Bulletin -